In the bowl of a stand mixer****,place warm water, yeast and 1 tablespoon sugar. Mix well and let stand for 5 minutes to proof the yeast.
Using the paddle attachment, add the warm milk, oil, beaten eggs, ube flavoring, sugar, 3 CUPS OF FLOUR and salt. Mix well to combine the ingredients, about 30 seconds. Switch to the dough hook then add remaining flour (reserve ½ cup) at once and knead. If the dough is still sticky, add flour 1 Tablespoon at a time until the dough is no longer sticky. Knead for 5 minutes or until smooth. Dough will be soft and a little tacky but won’t stick to your hands when touched.
Form the dough into a ball and coat with oil. Cover with a clean plastic wrap and let rise in a warm spot for an hour or until it doubles in size.
Combine the ingredients for the cheese filling into a bowl. Mash any lumps and stir until it turns into a smooth paste. Cover and refrigerate.
Punch the dough to release air bubbles and transfer to your work surface. Divide in half. Flatten each piece into a 1 / 2 inch thick rectangle and roll EACH dough tightly like a jelly roll, tucking it against itself in every turn. Pinch the edges to seal.
Divide each log into 15 pieces. Take a piece of dough and form into a ball by gathering all the edges together. Pinch to seal and place on the counter, seam side down. Do the same with the rest and cover with plastic wrap or a tea towel.
Remove the cheese filling from the fridge. Flatten each ball into a small circle and place a heaping teaspoon of cheese filling in the middle. Gather the edges and pinch very well to seal. Shape into a ball and roll in breadcrumbs. If using plain cheese cubes, just press the cheese gently on the ball of dough using your thumb and gather the edges to seal.
Place on the baking sheets spacing at least an inch apart to leave room for rising. Cover with plastic wrap. And let rise for 30 minutes or until almost double in size.
Preheat the oven to 315F and bake for 20mins**.